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Cosmological $\alpha$-attractors are a compelling class of inflationarymodels. They lead to universal predictions for large-scale observables, broadlyindependent from the functional form of the inflaton potential. In this work wederive improved analytical predictions for the large-scale observables, whosedependence on the duration of reheating and the parameter $\alpha$ is madeexplicit. We compare these with Planck and BICEP/Keck 2018 data in theframework of a Bayesian study, employing uniform logarithmic and linear priorsfor $\alpha$. Our improved universal predictions allow direct constraints onthe duration of reheating. Furthermore, while it is well-known that CMBconstraints on the tensor-to-scalar ratio can be used to place an upper boundon the $\alpha$ parameter, we demonstrate that including the$\alpha$-dependence of the scalar spectral tilt yields novel constraints on$\alpha$. In particular, for small $\alpha$, the scalar spectral tilt scaleswith $\log_{10}\alpha$, regardless of the specific potential shape. Fordecreasing $\alpha$, this eventually puts the models in tension with CMBmeasurements, bounding the magnitude of $\alpha$ from below. Therefore, inaddition to the upper bound from the tensor-to-scalar ratio, we derive thefirst lower bound on the magnitude of $\alpha$ for $\alpha$-attractor T-models,$\log_{10}{\alpha} = -4.2^{+5.4}_{-8.6}$ at $95\%$ C.L. .

Novel CMB constraints on the $\alpha$ parameter in alpha-attractor models